Question

(a) which of the following must be true about jims and melissas scores?
o both jim and melissa scored higher than the median.
o both jim and melissa scored below than the median.
o melissa scored higher than jim.
o jim scored higher than melissa.
(b) which of the following must be true about jims score?
o about 29% of the students who took the exam scored lower than jim.
o jim got about 29% of the questions correct.
o jims score was in the top half of all scores.
o jim missed 71 questions.

Explanation:

Step 1: Recall the definition of percentile

The \(n^{th}\) percentile means that \(n\%\) of the data is less than or equal to that value.

Step 2: Analyze part (a)

The median is the \(50^{th}\) percentile. Jim is at the \(29^{th}\) percentile (\(29\%<50\%\)) and Melissa is at the \(72^{nd}\) percentile (\(72\% > 50\%\)). So Melissa scored higher than the median and Jim scored below the median.

Step 3: Analyze part (b)

Since Jim is at the \(29^{th}\) percentile, about \(29\%\) of the students scored lower than Jim.

Answer:

(a) Melissa scored higher than the median and Jim scored below the median.
(b) About \(29\%\) of the students who took the exam scored lower than Jim.